Some linear feedback laws for stabilisation of sterile insect technique control system
Kala Agbo Bidi
TL;DR
This work addresses stabilizing mosquito populations under Sterile Insect Technique by designing linear feedback laws. It analyzes SIT models with states for the aquatic stage $E$, wild males $M$, fertilized females $F$, sterile counterparts $F_s$, $M_s$, and control input $u$, proving global stabilization to extinction under gain conditions. The authors develop two linear laws based on ($E$, $M+M_s$) and ($E$, $M$), employing Lyapunov functions and a helper function $\mathcal{H}(\psi)$ to establish exponential convergence, with explicit instantiations for practical deployment (e.g., $u(x)=2R(1-\nu)\nu_E E + (\delta_s-\delta_M)(M+M_s)$ and $u(x)=4R(\delta_s-\delta_M)M + 2R(1-\nu)\nu_E E$). The results enable simple, robust release strategies that can be implemented with field measurements (ovitraps and release-recapture) to support SIT programs in vector control and disease mitigation.
Abstract
The implementation of the Sterile Insect Technique (SIT) to manage a target population has been the focus of numerous recent scientific studies. The present work focuses on a feedback law that depends linearly on the state variables of the SIT control system. We provide both mathematical proof and numerical illustrations demonstrating the global asymptotic stability of the population to zero when releasing a number of sterile insects proportional to different state variables of the SIT model.